Date: March 2012

If 1 is a root of the equations *ay*^{2} + *ay* + 3 = 0 and *y*^{2} + *y* + *b* = 0 then *ab* equals: ?

A. 3

B. `-7/2`

C. 6

D. −3

Chapter: [2.03] Quadratic Equations

In Fig. 1, the sides AB, BC and CA of a triangle ABC, touch a circle at P, Q and R respectively. If PA = 4 cm, BP = 3 cm and AC = 11 cm, then the length of BC (in cm) is ?

A. 11

B. 10

C. 14

D. 15

Chapter: [3.01] Circles

In Fig. 1, the sides AB, BC and CA of a triangle ABC, touch a circle at P, Q and R respectively. If PA = 4 cm, BP = 3 cm and AC = 11 cm, then the length of BC (in cm) is ?

A. 11

B. 10

C. 14

D. 15

Chapter: [3.01] Circles

In Fig 2, a circle touches the side DF of ΔEDF at H and touches ED and EF produced at K and M respectively. If EK = 9 cm, then the perimeter of ΔEDF (in cm) is:

A. 18

B. 13.5

C. 12

D. 9

Chapter: [3.01] Circles

If the radius of the base of a right circular cylinder is halved, keeping the height the same, then the ratio of the volume of the cylinder thus obtained to the volume of original cylinder is:

1 : 2

2 : 1

1 : 4

4 : 1

Chapter: [7.02] Surface Areas and Volumes

If the area of a circle is equal to sum of the areas of two circles of diameters 10 cm and 24 cm, then the diameter of the larger circle (in cm) is:

A. 34

B. 26

C. 17

D. 14

Chapter: [3.01] Circles

The length of shadow of a tower on the plane ground is `sqrt3` times the height of the tower.

The angle of elevation of sun is:

A. 45°

B. 30°

C. 60°

D. 90°

Chapter: [4.01] Heights and Distances

If the coordinates of one end of a diameter of a circle are (2, 3) and the coordinates of its centre are (−2, 5), then the coordinates of the other end of the diameter are:

A. (−6, 7)

B. (6, −7)

C. (6, 7)

D. (−6, −7)

Chapter: [6.01] Lines (In Two-dimensions)

The coordinates of the point P dividing the line segment joining the points A (1, 3) and B (4, 6) in the ratio 2 : 1 are:

A. (2, 4)

B. (3, 5)

C. (4, 2)

D. (5, 3)

Chapter: [6.01] Lines (In Two-dimensions)

Two dice are thrown together. The probability of getting the same number on both dice is.

`A1/2`

`B1/3`

`C1/6`

`D1/12`

Chapter: [5.01] Probability

Find the value(s) of *k* so that the quadratic equation *x*^{2} − 4*kx* + *k* = 0 has equal roots.

Chapter: [6.01] Lines (In Two-dimensions)

Find the sum of all three digit natural numbers, which are multiples of 11.

Chapter: [2.02] Arithmetic Progressions

Tangents PA and PB are drawn from an external point P to two concentric circles with centre O and radii 8 cm and 5 cm respectively, as shown in Fig. 3. If AP = 15 cm, then find the length of BP.

Chapter: [3.01] Circles

In Fig. 4, an isosceles triangle ABC, with AB = AC, circumscribes a circle. Prove that the point of contact P bisects the base BC.

Chapter: [3.01] Circles

In Fig. 5, the chord AB of the larger of the two concentric circles, with centre O, touches the smaller circle at C. Prove that AC = CB.

Chapter: [3.01] Circles

The volume of a hemisphere is 2425`1/2cm^3`cm. Find its curved surface area?

Chapter: [7.02] Surface Areas and Volumes

In Fig. 6, OABC is a square of side 7 cm. If OAPC is a quadrant of a circle with centre O, then find the area of the shaded region. `[\text\ User=22/7]`

Chapter: [7.02] Surface Areas and Volumes

If the point A(0, 2) is equidistant from the points B(3, *p*) and C(*p*, 5), find *p*. Also, find the length of AB.

Chapter: [6.01] Lines (In Two-dimensions)

A number is selected at random from first 50 natural numbers. Find the probability that it is a multiple of 3 and 4.

Chapter: [5.01] Probability

Solve for x:

4x^{2} + 4bx − (a^{2} − b^{2}) = 0

Chapter: [2.03] Quadratic Equations

Solve for *x*: `3x^2-2sqrt6x+2=0`

Chapter: [2.03] Quadratic Equations

Prove that a parallelogram circumscribing a circle is a rhombus.

Chapter: [3.01] Circles

Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.

Chapter: [3.01] Circles

Construct a right triangle in which the sides, (other than the hypotenuse) are of length 6 cm and 8 cm. Then construct another triangle, whose sides are `3/5` times the corresponding sides of the given triangle.

Chapter: [3.03] Constructions

In Fig. 7, PQ and AB are respectively the arcs of two concentric circles of radii 7 cm and

3.5 cm and centre O. If ∠POQ = 30°, then find the area of the shaded region. [User`22/7`]

Chapter: [7.01] Areas Related to Circles

From a solid cylinder of height 7 cm and base diameter 12 cm, a conical cavity of same height and same base diameter is hollowed out. Find the total surface area of the remaining solid. [User `pi22/7`]

Chapter: [7.02] Surface Areas and Volumes

A cylindrical bucket, 32 cm high and with radius of base 18 cm, is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is 24 cm. Find the radius and slant height of the heap.

Chapter: [7.02] Surface Areas and Volumes

The angles of depression of two ships from the top of a lighthouse and on the same side of it are found to be 45° and 30° respectively. If the ships are 200 m apart, find the height of the lighthouse.

Chapter: [4.01] Heights and Distances

A point P divides the line segment joining the points A(3, -5) and B(-4, 8) such that `(AP)/(PB) = k/1`. If P lies on the line *x* + *y* = 0, then find the value of k.

Chapter: [6.01] Lines (In Two-dimensions)

If the vertices of ΔABC be A(1, -3) B(4, p) and C(-9, 7) and its area is 15 square units, find the values of p

Chapter: [6.01] Lines (In Two-dimensions)

A box contains 100 red cards, 200 yellow cards and 50 blue cards. If a card is drawn at random from the box, then find the probability that it will be (i) a blue card (ii) not a yellow card (iii) neither yellow nor a blue card.

Chapter: [5.01] Probability

The 17^{th} term of AP is 5 more than twice its 8^{th} term. If the 11^{th} term of the AP is 43, find its nth term.

Chapter: [2.02] Arithmetic Progressions

A shopkeeper buys some books for Rs 80. If he had bought 4 more books for the same amount, each book would have cost Rs 1 less. Find the number of books he bought.

Chapter: [1.01] Real Numbers

The sum of two numbers is 9. The sum of their reciprocals is 1/2. Find the numbers.

Chapter: [2.03] Quadratic Equations

Sum of the first 14 terms of and AP is 1505 and its first term is 10. Find its 25^{th} term.

Chapter: [2.02] Arithmetic Progressions

Prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact.

Chapter: [3.01] Circles

A quadrilateral ABCD is drawn to circumscribe a circle. Prove that AB + CD = AD + BC ?

Chapter: [3.01] Circles

A solid is in the shape of a cone surmounted on a hemisphere, the radius of each of them is being 3.5 cm and the total height of solid is 9.5 cm. Find the volume of the solid. (Use π = 22/7).

Chapter: [7.02] Surface Areas and Volumes

A bucket is in the form of a frustum of a cone and it can hold 28.49 litres of water. If the radii of its circular ends are 28 cm and 21 cm, find the height of the bucket. [Use`pi22/7` ]

Chapter: [4.01] Heights and Distances

The angle of elevation of the top of a hill at the foot of a tower is 60° and the angle of depression from the top of the tower to the foot of the hill is 30°. If the tower is 50 m high, find the height of the hill ?

Chapter: [4.01] Heights and Distances

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